论文标题
同质梯度孤子指标和相关方程的刚性
Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations
论文作者
论文摘要
我们证明了均匀空间的结构结果，这些空间支持非恒定解决方案对涉及函数的Hessian和一个不变的2 tensor的两个通用等式类别。我们还考虑这些系统的无微量版本。我们的结果概括了早期的刚性结果，梯度RICCI孤子和扭曲的产品爱因斯坦指标。特别是，我们的结果适用于任何不变曲率流的均匀梯度孤子，并为同型爱因斯坦指标提供了新的结构结果。
We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-tensor. We also consider trace-free versions of these systems. Our results generalize earlier rigidity results for gradient Ricci solitons and warped product Einstein metrics. In particular, our results apply to homogeneous gradient solitons of any invariant curvature flow and give a new structure result for homogeneous conformally Einstein metrics.
